In many types of modern communications systems, for example, radiotelephone communications systems, information is communicated using sequences of information symbols, e.g., bits. These symbol sequences typically are transmitted by modulating a radio-frequency carrier signal with the symbol sequence according to various types of pulse-modulation schemes, e.g., frequency-shift keying (FSK), binary phase-shift keying (BPSK), and the like. The modulated carrier signal typically is received at another location, and a complementary demodulator is used to recover the sequence from the modulated carrier signal.
The pulse-modulation techniques used to communicate symbol sequences typically suffer from a form of noise corruption referred to as intersymbol interference (ISI). ISI arises because of characteristics of the communications channel which induce phenomena such as delay spread and dispersion. In addition to ISI, a communications signal may also be subject to noise imparted by the various sources, e.g., interference from other transmission sources in the communications medium, transmitter-induced noise, receiver-induced noise, and the like. The noise in a communications signal often is "colored," i.e., correlated in time.
A well-known technique for producing an estimate of transmitted symbol sequence at a receiver is to process the received signal with a whitening filter and then perform sequential maximum likelihood sequence estimation (SMLSE) on the processed signal to estimate the original transmitted signal, as described in Forney, Jr., "Maximum Likelihood-Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interference," IEEE Transactions on Information Theory, Vol. IT-18, No. 3, pp. 363-378 (May 1972). As illustrated in FIG. 1, noisy communications signal 15 representing a symbol sequence 5 transmitted over a communications channel 10 and including additive noise 17 is input to an equalizer 20. In the equalizer 20, the signal 15 is passed through a so-called "whitening" matched filter 22 to produce a signal 23 in which the colored noise of the input signal 15 has been "whitened." The whitened signal 23 is then passed into an estimator 24 which produces an estimate 25 of the transmitted symbol sequence. The estimator 24 typically implements a process known as sequential maximum likelihood sequence estimation (SMLSE), also referred to as the Viterbi algorithm. The estimate 25 produced by the SMLSE performed in the estimator 24 represents an "optimal" estimate of the transmitted symbol sequence, the sense that the Viterbi algorithm produces an optimal estimate of the state sequence of a finite Markov process observed in the presence of memoryless noise, as described in Forney, Jr., "The Viterbi Algorithm," Proceedings of the IEEE, Vol. 61, pp. 268-278 (March 1973).
One drawback of this technique, however, is the complexity involved in producing the estimate 25. This complexity is attributable to the channel response of the equalizer 20, which includes the cascade of the whitening filter 22 and the estimator 24. The estimator 24 typically is designed to approximate the behavior of the communications channel 10. The whitening filter 22 typically has a relatively long time response compared to the estimator 24, thus resulting in a more complex and expensive equalizer 20 design.